The 27-year-old is set to become the Blades' first addition of the close season and his move - for a £3m fee plus add-ons - is expected to be completed later today.
Meanwhile, the Blades are also running the rule of former Manchester United and West Ham midfielder Ravel Morrison, who has linked up with the club on trial.
United have been known admirers of Freeman, previously linked with moves to Leeds United and Middlesbrough, for the past 12 months.
Speaking this morning, manager Chris Wilder said: "We are hoping Luke will become a Sheffield United player later on today.
"The two clubs are at it in conversations, but we are confident that it will go over the line and he will be our first signing."
Morrison, 24, currently without a club after leaving Ostersund, is training with the Blades this week and could join the squad on a pre-season tour to Portugal next week.
Wilder said: "We will talk and see how it goes. It could be a good fit for both. We’ll see how it goes."